CN112070200A - A Harmonic Group Optimization Method and Its Application - Google Patents

Abstract

The present disclosure provides a harmonic group optimization method and its application, and proposes a new continuous SSO integrated univariate update mechanism UM ₁ and a new harmonic step size strategy HSS, which improves the continuous simplified group optimization SSO, and UM ₁ and HSS can balance The exploration and utilization ability of continuous SSO in exploring high-dimensional multivariate and multimodal numerical continuous benchmark functions; the update mechanism UM1 only needs to update one variable, and it is completely different from the variables in SSO and does not need to update all variables; described in In UM1, HSS enhances the utilization capacity by reducing the step size based on harmonic sequences; numerical experiments are performed on 18 high-dimensional functions to confirm the efficiency of the method provided in this disclosure; the exploration of traditional ABC and SSO is improved It achieves an excellent balance between exploration and utilization, and has a wide range of applications, which can greatly improve the classification and prediction accuracy of newly acquired big data such as artificial neural networks and vector machines.

Description

A Harmonic Group Optimization Method and Its Application

technical field

The present disclosure relates to the technical fields of soft computing applications and big data processing, and in particular to a harmonic group optimization method and applications thereof.

Background technique

There are always a lot of optimization problems in practical applications, such as green supply chain management, big data and network reliability issues. It is also common to apply small variations (eg, integer variables, nonlinear equations, and/or multiple objectives) to the optimization model in real-world problems. However, even with just integer variables, these real-life problems become very difficult to solve, and would be much more complex and enormous to solve using traditional methods in acceptable time. As a result, the focus of various recent studies has shifted to producing high-quality solutions using soft computational methods rather than exact solutions within acceptable execution times, see refs [1-26].

More and more new soft computing methods are emerging, such as artificial neural network [2, 37], genetic algorithm (GA) [3, 4, 34], simulated annealing [5], tabu search [6], ant colony Optimization [11], particle swarm optimization algorithm [7, 8, 34], differential evolution [9, 10], algorithm estimation distribution [12], artificial bee colony algorithm (ABC) [13-16], simplified swarm optimization algorithm/ Simplified Swarm Algorithm (SSO) [17-26], Imperialist Competition Algorithm [35], Reinforcement Learning Algorithm [36], Bayesian Networks [38], Hurricane Optimization Algorithm [39], Gravity Search Algorithm [40] , Human Clustering [41], Bat Algorithm [42], Random Diffusion Search [43], etc. are all new soft computing methods inspired by natural phenomena that solve larger problems in science and technology in recent years. Therefore, soft computing has attracted noteworthy attention and has been applied to a range of real-world problems, such as swarm intelligence and evolutionary algorithms (EAs), respectively, see References [44] and [45].

In soft computing, the exploration based on local search is to find the optimal behavior in the neighborhood region of the known solution, improve the chance of solution quality at the cost of capturing the local optimal solution [2-26], and explore as The focused global search refers to searching for optimal values in an unexplored solution space to avoid getting stuck in local optima at the cost of running time [2-26]. Exploration and exploitation are opposites but complement each other. It is worth noting that a balance of exploration and exploitation is sought to ensure the realization of any soft computing approach.

The SSO (Simplified Swarm Optimization Algorithm/Simplified Swarm Optimization Algorithm) introduced by Yeh, see reference: [W.C.Yeh, "Study on Quickest Path Networks with Dependent Components and Apply to RAP", Technical Report NSC97-2221-E-007-099 -MY3, Distinguished Scholars ResearchProject granted by National Science Council, Taiwan] One of the newly proposed population-based soft computing methods. SSO obtains high efficiency and efficiency from existing known numerical experiments [17-26]. In addition, SSO can flexibly deal with various real-world problems and is gradually applied to different optimization applications, such as supply chain management [20, 21], redundancy allocation problems [18, 19, 27], data mining [20, 21], and Other optimization problems [32, 33].

The full variable update mechanism (UM _a ) is the basis for all variants of SSO, so all variables are updated in each solution. However, UM _a always explores the undiscovered solution space, and even if the best is close to the current solution [17-27, 31, 32], it may take extra time to reach the optimal state.

References involved in this disclosure:

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SUMMARY OF THE INVENTION

The present disclosure provides a harmonic group optimization method and its application. In order to propose a new continuous SSO integrated univariate update mechanism (UM ₁ ) and a new harmonic step size strategy (HSS), the ₁ ) and Harmonic Step Size Strategy (HSS) to improve Continuous Simplified Group Optimization (SSO). The described UM ₁ and HSS can balance the exploration and utilization capabilities of continuous SSO in exploring high-dimensional multivariate and multimodal numerical continuous benchmark functions; the update mechanism UM ₁ only needs to update one variable, and it is completely different from the one in SSO. Variables do not need to update all variables; in the described UM ₁ , HSS enhances the utilization capacity by reducing the step size based on the harmonic sequence. Numerical experiments were carried out on 18 high-dimensional functions to confirm the efficiency of the method provided by the present disclosure.

In order to achieve the above object, according to an aspect of the present disclosure, a harmonic group optimization method is provided, the method comprising the following steps:

Step 1, construct the harmonic step size strategy HSS;

Step 2, establishing a univariate update mechanism UM ₁ ;

In step 3, the optimized SSO is obtained by continuously simplifying the group optimization SSO through UM ₁ and HSS optimization;

Step 4, apply the optimized SSO to big data processing.

Further, in step 1, the method of constructing the harmonic step size strategy HSS is: in order to improve the exploration performance, the HSS based on the harmonic sequence is constructed as follows:

是floor函数/Floor()函数；将1,1/2,1/3,1/4,的序列称为谐波序列，则基于谐波序列HSS可表示如下：where _Nvar is the number of variables, Uk and _Lk are the upper and lower bounds of the _kth variable, i is the current algebra, k is the index of the current variable, and the notation

is the floor function/Floor() function; the sequence of 1, 1/2, 1/3, 1/4, is called the harmonic sequence, then based on the harmonic sequence HSS can be expressed as follows:

If each inherited cycle lasts for 50 generations, the value of the step size Δi _,k decreases from generation to generation from generation to generation.

gBest and some solutions are closer to the optimal state after long runs or multiple generations, and the updates of these solutions only need to change slightly to get closer to the optimal state without leaving the optimal region. As the harmonic sequence is reduced, the step size is adjusted from a longer time in the early generation to a shorter time in the later generation of the HSS, thus overcoming the defect of continuous SSO.

是通过修改X_j的x_j,k得到的时间解，可以得到以下等式：Further, in step 2, the method of establishing the univariate update mechanism UM ₁ is as follows: in the main soft calculation, each solution will be slightly updated, in order to reduce the random number and gradually change the stability of the solution, make each solution Only one randomly selected variable is updated in UM ₁ of , assuming i is the current generation number, x _{j, k} are variables randomly selected from the jth solution X _j ,

is the time solution obtained by modifying x _{j ,k} of X j, the following equation can be obtained:

σ _k,1 and σ _k,2 are uniform random variables generated in [-0.5, 0.5] and [0,1], respectively;

ρ _k is a uniform random variable generated in [0,1]; g _k represents the kth (k ^th ) variable of P _gBest ;

L _k and U _k are the lower and upper bounds of the kth variable, respectively.

Note:

(1) In the proposed UM ₁ of the present disclosure, the first subscript of each solution and the variables in UM _a are removed to reduce the running time, for example, X _i,j and x _i,j in UM _a , _k is simplified to X _j and x _j,k in the proposed UM ₁ .

(2) For simplicity without loss of generality, the formulation of the above equation is proposed considering the minimization problem.

的上述值如果在更新后不可行并且在代入X^*计算F(X^*)之前需要更改为其最近的 边界。(3)

The above value of if is not feasible after the update and needs to be changed to its nearest bound before substituting into X ^* to compute F(X ^* ).

For example, prepare to minimize the following equation:

gen为遗传的代数；

gen is the algebra of inheritance;

Among them, has the following properties:

Property 1: After implementing UM ₁ , the number of expected comparisons and random values in each solution is reduced from 3 N _var to 3 and N _var to 1.

Proof: The number that tests the feasibility of each update variable is one for both UM _a and UM ₁ . However, for each solution, UM _a tests each updated variable, while UM ₁ tests only one variable. Furthermore, for each solution, the expected number of comparisons for UM _a based on Eq. (4) is calculated as follows:

N _var ·(3c _w +2c _g +c _r )≥N _var ·(3c _w +3c _g +3c _r )=3·N _var ,

Because cr <c _w <c _g and _cr +c _w +c _g =1 and it is related to the probabilities of c _g , c _w and _cr in the first, second and third terms of equation (4 ₎ After 1, 2 and 3 comparisons, we get:

(c _g +2c _w +3c _r )≤(3c _g +3c _w +3c _r )=3.

Further, in step 3, the method for obtaining the optimized SSO by continuously simplifying the group optimization SSO by UM ₁ and HSS optimization is: The improved continuous SSO method proposed by the present disclosure is described as follows:

Step 0, let i=j=gBest=1.

Step 1, pass X _j and calculate F(X _j );

Step 2, if F(X _gBest )<F(X _j ) then let gBest=j;

Step 3, if j<N _sol , let j=j+1 and go to step 1;

其中，k＝1,2,…,N_var；Step 4, let n ^* =1, N ^* =50, and let

Wherein, k=1,2,..., _Nvar ;

Step 5, let i=i+1 and j=1;

Step 6, randomly select a variable from X _j , such as x _j,k ;

Step 7, let

Step 8, let

Step 9, if F(X ^* )<F(Xj) then make _{Xj =} X ^* and go to step 10, otherwise go to step 11;

Step 10, if F(X _j )<F(X _gBest ), let gBest=j;

Step 11, if the current running time is equal to or greater than T, the process ends, and X _gBest is the final solution suitable for F(X _gBest );

Step 12, if j<N _sol then let j=j+1, and go to step 6;

Step 13. If i<N ^* then go to step 5;

其中，k＝1,2,…,N_var,并转到步骤5，Step 14. Increase n ^* by 1, increase N ^* by 50, and let

where k=1,2,...,N _var , and go to step 5,

为最佳的第k个变量，x_i,j,k为第j个解中第k个变量的当前值， δ<<Δ_k，Δ_k为步长，δ与Δ_k的关系例如，如果δ＝100·Δ_k是最好的情况，x_i,j,k将需要100代才能 收敛到

in,

is the optimal kth variable, x _i,j,k is the current value of the kth variable in the jth solution, δ<< _Δk , _Δk is the step size, the relationship between δ and _Δk For example, if δ=100· _Δk is the best case, x _i,j,k will take 100 generations to converge to

Further, in step 4, the application method of the optimized SSO application in big data processing by artificial neural network is:

Step A1, collecting big data that conforms to the big data type;

Step A2, preprocessing and cleaning the collected big data, and then extracting the data set obtained after the big data cleaning;

Step A3, dimensionality reduction is performed on the data set obtained after cleaning;

Step A4, dividing the data set after dimensionality reduction into a data set into a training set and a test set;

Step A5, determine an artificial neural network with a structure of 6-5-1 three-layer perceptron neural network, the neural network needs a total of 41 parameters to be optimally designed, and the value range of the optimal design parameters of the neural network is [-1,1 ];

Step A6, determine that the input variable of the artificial neural network is the big data that meets the big data type, and the output variable of the artificial neural network is the big data output;

Step A7, determine the input variable and the output variable of the artificial neural network;

Step A8: Decode the variables in X _j in each optimized SSO into the parameters to be optimized by the artificial neural network, calculate the error of the neural network after training the training set and/or the test set, and calculate the calculated error. As the fitness F(X _j ), it is input into the optimized SSO, and the final solution X _gBest suitable for F(X _gBest ) obtained from the operating results of the optimized SSO (the operating results of step 0 to step 14) is decoded is the parameter of the artificial neural network, and the obtained artificial neural network is used as the classification model;

Step A9, classifying the newly collected big data conforming to the big data type by the classification model;

Among them, the big data that conforms to the big data type includes but is not limited to any kind of big data that conforms to the data type: traditional enterprise data, machine and sensor data, and social data; traditional enterprise data includes consumer data of CRM systems, traditional ERP data data, inventory data, and accounting data, etc. Machine and sensor data includes call records, smart meters, industrial equipment sensors, equipment logs, transaction data, and more. Social data includes user behavior records, feedback data, etc. Social media platforms like Twitter, Facebook.

The big data output includes, but is not limited to, the confidence level of the data category and the predicted value for any period of time in the future.

The application of the optimized SSO can greatly improve the classification accuracy or prediction ability of artificial neural network in newly acquired big data.

Further, the method of applying the optimized SSO in big data processing through support vector machine is:

Step B1, collecting big data conforming to the big data type;

Step B2, preprocessing and cleaning the collected big data and extracting features to obtain the feature vector of the big data;

Step B3, the feature vector of the big data is used as the training data set;

Step B4, randomly generate j uniform random variables, the set of random variables is X _j , and each randomly selected variable in X _j stores the penalty factor C of the support vector machine and the radial basis kernel parameter g;

Step B5: Calculate the fitness F(X _j ) of X _j , input it into the optimized SSO, and use the optimized SSO operation result (the operation result of step 0 to step 14) to obtain the suitable F(X _gBest ) The final solution X _gBest is decoded into the parameters of the support vector machine, and the obtained support vector machine is used as the classification model;

Step B6, classifying the newly collected big data conforming to the big data type by the classification model;

Among them, the big data that conforms to the big data type includes but is not limited to any kind of big data that conforms to the data type: traditional enterprise data, machine and sensor data, and social data; traditional enterprise data includes consumer data of CRM systems, traditional ERP data data, inventory data, and accounting data, etc. Machine and sensor data includes call records, smart meters, industrial equipment sensors, equipment logs, transaction data, and more. Social data includes user behavior records, feedback data, etc.

Among them, the big data output includes but is not limited to data classification results and category confidence.

The application of the optimized SSO can greatly improve the classification accuracy of the newly acquired big data by the support vector machine.

The beneficial effects of the present disclosure are as follows: the present invention provides a harmonic group optimization method and its application, improves the performance of exploration and utilization of traditional ABC and SSO, and obtains a comparison between exploration and utilization Excellent balance point, and has a wide range of applications, can be applied in artificial neural network, genetic algorithm (GA), simulated annealing, tabu search, ant colony optimization, particle swarm optimization algorithm, differential evolution, algorithm estimation distribution, artificial bee colony algorithm ( ABC), imperialist competition algorithm, reinforcement learning algorithm, Bayesian network, hurricane optimization algorithm, gravitational search algorithm, human swarming, bat algorithm, random diffusion search and other methods for seeking optimization solutions, parameters and other variables are optimized by the method of the present disclosure After adjustment, it can be directly applied to the fields of big data processing, image processing, audio and video recognition, etc., which can greatly improve the classification and prediction accuracy of newly acquired big data such as artificial neural networks and vector machines; improve the performance of image processing, audio and video. Accuracy and speed of recognition.

Description of drawings

The above-mentioned and other features of the present disclosure will become more apparent from the detailed description of the embodiments shown in conjunction with the accompanying drawings, in which the same reference numerals refer to the same or similar elements of the present disclosure. The drawings are only some embodiments of the present disclosure. For those of ordinary skill in the art, other drawings can also be obtained from these drawings without creative efforts. In the drawings:

Figure 1 is a bar graph of the average success rate of SSO1 under different Δ and T values in experiment 1;

Figure 2 is a bar graph of the average success rate of SSO1 and the problems in Experiment 1 under different Δ values and problems;

Figure 3 is a bar graph of F _min values obtained from ABC, GA, PSO, SSO1 and SSOa in Experiment 2;

Figure 4 is a histogram of AIO (ABC, SSO1), AIO (SSOa, SSO1), and AIO (ABC, SSOa);

Figure 5 is a bar graph of the success rate under different T values in experiment 2;

Figure 6 is a bar graph of the F _min value of ABC, SSO1, and SSOa in experiment 2;

Figure 7 is a box plot of the average fitness values of ABC, SSO1 and SSOa when T=1.25 in experiment 2;

Figure 8 is a box plot of the average fitness values of ABC, SSO1 and SSOa when T=1.50(a) in experiment 2;

Figure 9 is a box plot of the average fitness values of ABC, SSO1 and SSOa when T=1.50(b) in experiment 2;

Figure 10 is a box plot of the average fitness values of ABC, SSO1 and SSOa when T=1.75 in experiment 2;

Figure 11 is a box plot of the average fitness values of ABC, SSO1 and SSOa when T=2.00 in experiment 2;

Figure 12 is a box plot of the average fitness values of ABC, SSO1 and SSOa when T=2.25 in experiment 2;

Figure 13 is a box plot of the average fitness values of ABC, SSO1 and SSOa when T=2.50 in experiment 2;

Figure 14 is a box plot of the average fitness values of ABC, SSO1 and SSOa when T=2.75 in experiment 2;

Figure 15 is a box plot of the average fitness values of ABC, SSO1 and SSOa when T=3.00 in experiment 2;

Figure 16 is a box plot of the average fitness values of ABC, SSO1 and SSOa when T=3.50 in experiment 2;

Figure 17 is a boxplot of the average fitness values of ABC, SSO1 and SSOa at T=3.75 in Experiment 2.

Detailed ways

The concept, specific structure and technical effects of the present disclosure will be clearly and completely described below in conjunction with the embodiments and the accompanying drawings, so as to fully understand the purpose, solutions and effects of the present disclosure. It should be noted that the embodiments in the present application and the features of the embodiments may be combined with each other under the condition of no conflict.

Simplified Swarm Optimization (SSO) overview:

The method of continuous SSO processing variables is shown in References [23-25].

On the basis of traditional SSO, a new continuous SSO is proposed. Hereinafter, before presenting the new SSO proposed by the present disclosure, the conventional SSO is briefly introduced.

Traditional (Discrete) SSO

Traditional (discrete) SSO is very efficient at solving discrete (optimization) problems (discrete variables only) [17-21, 32] or continuous problems with finite floating-point numbers [22], e.g., the number of values per function in the data Limited in mining problems.

The basic idea of all types of SSO is that each variable, say x _i+1,j,k , needs to be updated according to the following equation:

where x is a randomly generated feasible value. For details, see references [17-27, 31, 32].

c _g , c _p , and c _w are parameters.

Based on the step function shown in equation (1) and the generated random number ρ _k , discrete SSO updates each variable by validating the first to last term in the step function until it finds a random number containing the generated random number interval.

Discrete SSO only updates each variable to a low probability value that has never been seen before, i.e. _cr . Therefore, in most cases, discrete SSO can only update a variable to a limited number of values, namely gBest, pBest, and itself, and these values are only found among all previous values. update process. The above advantages make discrete SSO very effective in solving discrete problems, see References [17-22, 32].

Continuous SSO:

For a general continuous optimization problem, every variable of the final solution in the continuous optimization problem may never be found in all previous update processes. Therefore, discrete SSO needs to be modified for continuous problems without losing the simplicity and convenience of discrete SSO [23-27,32]. Note that the advantages of continuous SSO are exactly the disadvantages of discrete SSO, and vice versa.

The basic flow of SSO variables has never changed, but is based on the step function of updating the variables listed in Equation (1), see References [17-27, 31, 32]. So far, the main trend to develop continuous SSO is to add a step function to some terms in equation (1) (see refs [23–25]), or to combine SSO with other soft computing methods [23–25]. 26, 27, 31], such as differential evolution (see refs [26, 31]) and PSO (see refs [C.L. Huang, "A particle-based simplified swarm optimization algorithm for reliability redundancy allocation problems", Reliability Engineering & System Safety, vol. 142, pp. 221-230, 2015]).

The fully variable update mechanism in SSO (e.g., equation (1)) is able to escape local optimization and explore unreached/unrealized spaces. So the goal of continuous SSO is to explore better ways in exploration, the main step is to add a random step size in some terms of the update mechanism, which is obtained by multiplying the step size by some random number. Our main purpose for this disclosure will be to explore better step sizes, as the method identified in this disclosure.

Yeh first proposed a continuous SSO by adding a step length to the update mechanism for prediction of time series problems. See reference (W.C.Yeh, "A New Parameter-Free Simplified Swarm Optimization for Artificial Neural Network training and its Application in Prediction of Time- Series”, IEEE Transactions on Neural Networks and Learning Systems, vol.24, pp.661-665, 2013), as follows

where _σk is a uniform random number generated in the range [-1,1], and the step size _Δj is the reciprocal of the genetic algebra for which the fitness of the ith solution is not improved.

Note that Equation (2) is also the first adaptive parameter concept, which takes the parameters c _g (denoted as c _g,i,j in Equation (2)) and cw (denoted as c _{w ,i} in Equation (2)) _,j ) as variables such that each solution has its own c _g and c _w in SSO. See reference [WCYeh, "A New Parameter-Free Simplified Swarm Optimization for Artificial NeuralNetwork training and its Application in Prediction of Time-Series", IEEE Transactions on Neural Networks and Learning Systems, vol.24, pp.661-665, 2013] , this concept is different from traditional SSO, all parameters of SSO are fixed from start to end.

并在方程(2)中再乘以一个随机数，(见参考文献【K.Kang,C.Bae,H.W.F. Yeung,and Y.Y.Chung,“A Hybrid Gravitational Search Algorithmwith Swarm Intelligence and Deep Convolutional Feature for Object TrackingOptimization”,Applied Soft Computing, https://doi.org/10.1016/j.asoc.2018.02.037,2018】)，如下。In order to determine that the value of the step size _Δj is still too large [23, 24] even for a larger number of generations in Eq. (2), Yeh proposed a new UM (here called UM _a ) to update all continuous variables by shortening interval [-1,1] to [-0.5,0.5], change Δ _j to

and multiplied by a random number in equation (2), (see references [K. Kang, C. Bae, HWF Yeung, and YY Chung, "A Hybrid Gravitational Search Algorithm with Swarm Intelligence and Deep Convolutional Feature for Object TrackingOptimization", Applied Soft Computing, https://doi.org/10.1016/j.asoc.2018.02.037, 2018]), below.

in,

c _g , _cr are parameters, N _var is the number of variables. σ _1,k and σ _2,k are two uniform random variables generated in [-0.5, 0.5];

ρ _k is a uniform random variable generated in [0,1]; U _k and L _k are the upper and lower bounds of the kth variable.

In Equation (3), the solution can only be updated to a better value; otherwise, UM _a retains the original solution before updating Equation (4) is the most important part of UM _a , the concept behind it is that each variable is updated to Its own neighborhood, the neighborhood of _gBest , and the interval between itself and _gBest (if ρ _k is in the binomial) and c _w =1- _{cr-c g (} the third term in equation (4)) within the interval).

Note:

1. Equation (4) corrects the error in Reference [25], which is the loss of ρ _2,var .

2. In Eq. (4), if the updated variable is not feasible, it is set to the nearest boundary.

The disadvantages of current continuous SSO are:

In the existing continuous SSO proposed in refs [23–25], the step sizes are all fixed, and each variable requires the step size of all genetic algebras.

Starting from equation (2), the minimum value of the random step size ρ _k ·Δ _j is 1/N _gen , only when ρ _k =-1 and 1/Δ _j =N _gen , that is, the jth solution is not changed from the beginning to the end. Improve. For example, if N _gen =1000, then ρ _k ·Δ _j =-0.001. For some special problems, the above values are still too large and therefore too far from optimal.

In equations (4) and (5), when the current algebra approaches its late end point, if the step size _Δk is too long, the update mechanism cannot be utilized to make it converge to the optimal value. Conversely, if the step size _Δk is too short and the momentum of the solution is insufficient, it will take a long time to get around the optimal value, especially in the early stages.

如 果δ<<Δ_k甚至Δ_k需要计算在[-0.5，0.5]内生成的两个不同的随机数，则下一个更新的解接近 最优的可能性很小。然而，如果δ＝100·Δ_k是最好的情况，x_i,j,k将需要100代才能收敛到

For example, let the current value of the kth variable in the jth solution be x _i,j,k , and the best kth variable is

If δ<< _Δk or even _Δk needs to compute two different random numbers generated within [-0.5, 0.5], there is little chance that the next updated solution will be close to optimal. However, if δ=100· _Δk is the best case, x _i,j,k will take 100 generations to converge to

Therefore, it is more reasonable to have an adaptive step size instead of a fixed step size in exploration. Therefore, the present disclosure proposes a new HSS-based continuous SSO update mechanism.

UM ₁ and HSS proposed by this disclosure:

In order to improve the exploration performance, the harmonic sequence-based HSS proposed in the present disclosure is presented in equation (6) as follows:

是floor函数/Floor()函数。where _Nvar is the number of variables, Uk and _Lk are the upper and lower bounds of the _kth variable, i is the current algebra, k is the index of the current variable, and the notation

is the floor function/Floor() function.

If the sequence of 1, 1/2, 1/3, and 1/4 is called a harmonic sequence, the harmonic sequence-based HSS proposed by the present disclosure can be expressed as follows:

If each genetic cycle lasts for 50 generations. The value of the step size Δi _,k decreases from generation to generation from generation to generation. Table 1 shows the step size based on HSS (if Uk- _Lk =10 and _{Nvar =} 100).

Table 1 20 steps

period i 1 2 3 4 5 6 7 8 9 10 Δ_i,k 0.08000 0.04000 0.02667 0.02000 0.01600 0.01333 0.01143 0.01000 0.00889 0.00800 period i 11 12 13 14 15 16 17 18 19 20 Δ_i,k 0.00727 0.00667 0.00615 0.00571 0.00533 0.00500 0.00471 0.00444 0.00421 0.00400

gBest and some solutions are closer to optimal after long runs or multiple generations. The updates of these solutions only need to change slightly to get closer to the optimal state without leaving the optimal region. Due to the reduced harmonic sequence, the step size is adjusted from a longer time in the early generation to a shorter time in the later generation of the HSS, thus overcoming the defect of continuous SSO.

Univariate UM (UM ₁ )

In major soft computations, each solution is updated slightly. For example, PSO's UM is a vector-based UM as the two equations listed below, specifically (see References [7, 8, 27]):

V _i+1,j =wV _i,j +c ₁ ·σ ₁ ·(GX _i,j )+c ₂ ·σ ₂ ·(P _i -X _i,j ) (8)

X _i+1,j =X _i,j +V _i+1,j (9)

where _Vi,j and X _i,j are the velocity and position of the jth particle in the ith generation, respectively;

w, c ₁ , c ₂ are constants; σ ₁ and σ ₂ are two uniform random variables generated in the interval [0,1]; P _i is the pBest of the solution i;

G=P _gBest is gBest. Note: P _gBest in SSO is equal to G in equation (8).

In ABC (see References [13-16]), a variable is randomly selected for each solution to update. The update operator in the traditional genetic algorithm (GA) (see References [3, 4]) can change half of the variables through a cut-point crossing, or update two variables through a cut-point mutation. However, in SSO, all variables must be updated.

是通过修改X_j的x_j,k得到的时间解。可以得到以下等式：To reduce random numbers and gradually change the stability of the solution, only one randomly selected variable is updated in UM ₁ for each solution. Suppose i is the current generation number, x _j,k are variables randomly selected from the jth solution X _j ,

is the time solution obtained by modifying x _j,k of X _j . The following equation can be obtained:

σ _k,1 and σ _k,2 are uniform random variables generated in [-0.5, 0.5] and [0,1], respectively;

ρ _k is a uniform random variable generated in [0,1];

L _k and U _k are the lower and upper bounds of the kth variable, respectively.

Note:

(1) In the proposed UM ₁ of the present disclosure, the first subscript of each solution and the variables in UM _a are removed to reduce the running time, for example, X _i,j and x _i,j in UM _a , _k is simplified to X _j and x _j,k in the proposed UM ₁ .

(2) For simplicity without loss of generality, the formulation of the above equation is proposed considering the minimization problem.

的上述值如果在更新后不可行并且在代入X^*计算F(X^*)之前需要更改为其最近的 边界。(3)

The above value of if is not feasible after the update and needs to be changed to its nearest bound before substituting into X ^* to compute F(X ^* ).

For example, prepare to minimize the following equation:

Table 2 lists the updated X ₇ based on different p ₁ values for the proposed UM ₁ .

Table 2 Example of UM ₁

替换

Mark ^! For starting from 1.216>U ₁ =1.0

replace

Mark ^{! !} To replace gBest=3 with gBest=7 starting from F(X ₇ )=F(-0.41467,-0.3)=0.008395<F(X _gBest )=F(-0.5,-0.9)=0.0596.

Therefore, the following lemma is true.

Property 1: After implementing UM ₁ , the number of expected comparisons and random values in each solution is reduced from 3 N _var to 3 and N _var to 1.

Proof: The number that tests the feasibility of each update variable is one for both UM _a and UM ₁ . However, for each solution, UM _a tests each updated variable, while UM ₁ tests only one variable. Furthermore, for each solution, the expected number of comparisons for UM _a based on Eq. (4) is calculated as follows:

N _var ·(3c _w +2c _g +c _r )≥N _var ·(3c _w +3c _g +3c _r )=3·N _var , (15)

Because cr <c _w <c _g and _cr +c _w +c _g =1 and it is related to the probabilities of c _g , c _w and _cr in the first, second and third terms of equation (4 ₎ After 1, 2 and 3 comparisons, we get:

(c _g +2c _w +3c _r )≤(3c _g +3c _w +3c _r )=3, (16)

If UM ₁ is implemented based on equation (11), σ _var,1 , σ _var,2 and ρ _var are required for each variable in equation (4), but only for each variable in equation (11).

The improved continuous SSO method proposed by the present disclosure is described as follows:

Step 0, let i=j=gBest=1.

Step 1, create any X _j and calculate F(X _j );

Step 2, if F(X _gBest )<F(X _j ) then let gBest=j;

Step 3, if j<N _sol , let j=j+1 and go to step 1;

其中，k＝1,2,…,N_var；Step 4, let n ^* =1, N ^* =50, and let

Wherein, k=1,2,..., _Nvar ;

Step 5, let i=i+1 and j=1;

Step 6, randomly select a variable from X _j , such as x _j,k ;

Step 7, let

Step 8, let

Step 9, if F(X ^* )<F(Xj) then make _{Xj =} X ^* and go to step 10, otherwise go to step 11;

Step 10, if F(X _j )<F(X _gBest ), let gBest=j;

Step 11, if the current running time is equal to or greater than T, the process ends, and X _gBest is the final solution suitable for F(X _gBest );

Step 12, if j<N _sol then let j=j+1, and go to step 6;

Step 13. If i<N ^* then go to step 5;

其中，k＝1,2,…,N_var,并转到步骤5。Step 14. Increase n ^* by 1, increase N ^* by 50, and let

where k=1,2,..., _Nvar , and go to step 5.

为最佳的第k个变量，x_i,j,k为第j个解中第k个变量的当前值，δ<<Δ_k， Δ_k为步长，δ与Δ_k的关系例如，如果δ＝100·Δ_k是最好的情况，x_i,j,k将需要100代才能收敛到

in,

is the optimal kth variable, x _i,j,k is the current value of the kth variable in the jth solution, δ<< _Δk , _Δk is the step size, the relationship between δ and _Δk For example, if δ=100· _Δk is the best case, x _i,j,k will take 100 generations to converge to

Example performance evaluation:

In this example, based on 18 50-variable continuous numerical functions extended from the benchmark problem (see References [13-16, 26, 25], two experiments, Experiment 1 and Experiment 2, were carried out, as shown in the experimental data in Table A. Show. Data type markers in the experimental data in Table A include C: characteristic data, U: unimodal data, M: multimodal data, S: separable data, N: non-separable data.

Table A Experimental data

experimental design:

For easy identification, reference [25] (K.Kang, C.Bae, H.W.F.Yeung, and Y.Y.Chung, "AHybrid Gravitational Search Algorithm with Swarm Intelligence and DeepConvolutional Feature for Object Tracking Optimization", Applied SoftComputing, https:// The SSO of UMa proposed in doi.org/10.1016/j.asoc.2018.02.037, 2018) is called SSOa, and the SSO implemented by HSS and UM1 in this embodiment is called SSO1 in this embodiment.

In Experiment 1, only the effect of HSS and different related step size strategies were tested to determine the optimal value of step size in the proposed HSS. The step size with the best results in Experiment 1 was used in SSO1 of Experiment 2.

In Experiment 2, the focus shifts to comparing the performance of SSO1 with four other algorithms: ABC [13-16], SSOa [25], GA [3,4] and PSO [7,8]; GA and PSO are evolutionary computation and two state-of-the-art algorithms in swarm intelligence; ABC [13-16] and SSOa [25] are the most common algorithms among 50 well-known benchmark problems if the stopping criteria are the number of fitness function evaluations and the running time, respectively, Its variable is less than or equal to 30.

Every algorithm tested in all experiments is written in the C programming language. Among them, the ABC code is adapted from http://mf.erciyes.edu.tr/abc/.

SSOa, GA and PSO are all from http://integrationandcollaboration.org/SSO.html. Each test was applied to an Intel Core i7-5960X CPU 3.00GHz, 16GB RAM, and 64-bit Win10, with runtime in CPU seconds.

In all tests, all parameters applied in SSO1, SSOa and ABC during the experiment were taken directly from ref. [25] for a more accurate comparison: _{cr = 0.45, c g =} 0.40, c _w = 0.15.

For ABC, references [13-16] were adopted for all parameters. The colony size is 50, the number of food sources is 25, and if there is no improvement after 50 25 = 750 updates, regenerate the solution.

For GA, one-point crossover, two-point mutation and elite selection were achieved with a crossover rate of 0.7 and a mutation rate of 0.3, respectively, see refs [3,4].

For PSO, c _w =0.9 and c ₁ =c ₂ =2.0 in equation (4); if the value of the velocity function is greater than 2 or less than -2, set the velocity function in the range of 2 or -2 See Ref. [7,8].

In each generation, ABC may calculate the fitness value more than once, see References [13-16], therefore, it is incorrect and unfair to use the genetic generation as the stopping criterion.

Also, the second UM in ABC, "the onlooker", takes extra time to update the solution.

Therefore, for a fair comparison, time limits (denoted by t) of 1.25, 1.50... to 3.75 computer seconds for each algorithm in Experiment 2 were used as stopping criteria to observe trends and changes in each algorithm.

NOTE: Each run is independent for all three algorithms. For example, in the case of t=1.50, each run of SSO1 must restart from 0 seconds, rather than simply extending from t=1.25 times 0.25 seconds to any run

For each benchmark function, the average run time is the time to get 50gBest. In all tables, each subscript represents the rank of the value. Furthermore, N _run =55 and N _sol =100.

In practical applications, the algorithm is implemented and executed many times to find the best result. Only the solution with the best result is kept and used. Therefore, most relevant published papers simply report and compare the best results obtained from the algorithms to demonstrate the properties, see refs [13-16, 25, 27]. Therefore, the present disclosure also focuses on the best result _Fmin in Experiment 2 as well.

Experiment 1: Find the optimal step size Δ:

The experimental results of Experiment 1, including F _avg , F _min , F _max , F _std success rate (the percentage of cases that successfully solve the problem), and the number of fitness function calculations obtained based on step size Δ=1.0 for Experiment 1, in T = 1.25, 1.50, ..., 1.25 and 1.50 for 55 runs in 3.70 seconds, as shown in Table 3 and Figures 1 and 2 for different delta values and T in Experiment 1 Figure 2 shows the average success rate of SSO1 under different Δ values and problems and the problems in Experiment 1.

Although all correlation values in Table 3 tend to decrease as T increases, some fluctuations are found, eg, F _avg = 0.04467947084586 at T = 2.00 improves to 0.03980129242576 at T = 2.25, and then decreases at T = 2.50 at Δ = 1.25 Up to 0.06607165055859, this fluctuation is due to the randomness of soft computation and that each run is independent.

From Table 3, it can be seen that Δ=1.25 has the best _Fmin for _T≥2.00 (except for T=3.50), and the best _Favg , Fmax and _Fstd for T=1.50, 2.00, 2.25 and 2.75; for T =1.75, 3.25 and 3.50, Δ=1.00 has the best _Favg , _Fmin , Fmax and _Fstd (except _Fmin at T=3.25 ₎ ; for _Favg , _Fmax and _Fstd , Δ=1.75 is Optimal values for minimum and maximum T, namely T=1.25 and T=3.75.

Table 3 Results obtained from different Δ values in Experiment 1

Figures 1 and 2 show the average success rates for different t values and benchmark problems, respectively. Success rate is defined as the percentage that the final gBest is equal to the optimal solution. For example, a 62.020% success rate means, 100·55·18=99,000 for Δ=1.25 and t=1.25, 62.020% of the final gBest equals the relevant optimization, where N _sol = 100 and N _run = 55, where 18 is the number of benchmark questions.

From the above it can be observed that Δ=1.25 always has the best average success rate for different T values and benchmark problems in Figures 1 and 2. Note that the difference between Δ=1.25 and Δ=1.00 and between Δ=1.25 and Δ=1.50 is as high as 27%, ie, Δ=1.25 has a 27% higher probability of obtaining the best value than Δ=1.00 and Δ=1.50. SSO1 at Δ = 1.25 is able to solve 14 of the 18 benchmark problems, which is also the best of the three settings for Δ.

From Table 3 and Figures 1 and 2, Δ=1.25 is better than 1.00 and 1.50 in terms of the quality of the solution. Therefore, Δ=1.25 was used in the proposed HSS and Experiment 2 without further optimization of Δ.

Experiment 2: Comparison between ABC, GA, PSO, SSO1 and SSOa:

The mean values of F _min obtained from the five tested algorithms (i.e. ABC, GA, PSO, SSO1 and SSOa) from 55 runs in T = 1.25, 1.50, ..., 3.70 seconds are shown in Figure 3 shown in Figure 3 are the F _min values obtained from ABC, GA, PSO, SSO1 and SSOa in Experiment 2. The results obtained from ABC, SSO1 and SSOa as shown in Fig. 7, Fig. 8, Fig. 9, Fig. 10, Fig. 11, Fig. 12, Fig. 13, Fig. 14, Fig. 15, Fig. 16, Fig. 17, respectively, are Boxplots of the average fitness values of ABC, SSO1 and SSOa when the values of T in experiment 2 are 1.25, 1.50(a), 1.50(b), 1.75, 2.00, 2.25, 2.50, 2.75, 3.00, 3.50, 3.75, respectively The 11 boxplots of , are shown together in Figure 6, which is a bar graph of F _min values for ABC, SSO1, and SSOa in Experiment 2, which graphically depicts the overall results. NOTE: These 11 boxplots also show the best results. Additionally, the third quartile to mean worst-fit results were truncated in order to obtain more detail about the essential part of the results (average from best quartile to third quartile).

Average F _min improvement (AIO) using SSO1 with ABC and SSOa, such as AIO (ABC, SSO1) and AIO (SSOa, SSO1), as shown in Figure 4, Figure 4 for AIO (ABC, SSO1), AIO (SSOa) , SSO1), and AIO (ABC, SSOa) histograms.

其中，α,β均表示测 试算法；in,

Among them, α and β both represent the test algorithm;

The associated success rates are summarized in Figure 5, which is a bar graph of the success rates at different T values in Experiment 2. The number of fitness function calculations is shown in Table 4.

Furthermore, some fluctuations were observed in some results of Experiment 2. These fluctuations are caused by the random nature of soft computing and the fact that each run is independent.

Table 4 Number of fitness function calculations in Experiment 2

Comprehensive analysis of the quality of the solution

Figures 3, 6, and 7 highlight the effectiveness (i.e., the quality of the solution) of ABC, SSO1, and SSOA. As can be seen from Figure 3, the performance of both the genetic algorithm and the particle swarm algorithm is much worse than the other three algorithms. This observation was made in other studies [13-16]. Furthermore, the weaknesses of genetic algorithms and particle swarm algorithms become more apparent as the running time increases. Therefore, the remainder of this disclosure focuses only on ABC, SSO1 and SSOA.

As shown in Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, the values of T in Experiment 2 are 1.25, 1.50, 1.50, respectively , 1.75, 2.00, 2.25, 2.50, 2.75, 3.00, 3.50, 3.75 The boxplots of the average fitness values of ABC, SSO1, and SSOa, as the running time increases, the results are closer to the optimal solution. As can be seen from Figure 6, which is a bar graph of F _min values for ABC, SSO1, and SSOa in Experiment 2, ABC is better than SSO1 and SSOa for smaller runtimes, for example, T=1.25 and T=1.50 . However, due to modern advanced computer technology, the relevance of the smaller "run time" is not important. In contrast, SSO1 outperformed ABC after T > 2.75 seconds, while SSOa outperformed the average _Fmin for all Ts. For T=3.75, the gap between SSO1 and ABC is almost 0.01, and the gap between SSO1 and SSOa is almost 0.005. Furthermore, ABC's _SSO1 for Favg did not increase to the same extent as T increased. The above results provide evidence that ABC is easily trapped in local optima for large T.

As shown in Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17,

ABC yields better _{Fmax and Fstd values} . Conversely, _SSOa produces the worst values for Fmax and _Fstd . The reason for this result is that UMa used in SSOa has to update all variables, whereas only one variable is selected in ABC, and UM1 is used in SSO1 for each solution of each generation. Another reason why ABC is always stronger than SSO1 and SSOa is that ABC is prone to local traps and lacks the ability to escape local optima.

In conclusion, the SSO1 method proposed in the present disclosure has obvious advantages over other methods.

Average F _min improvement rate (AIO)

To measure the amount of improvement in average Fmin obtained from ABC, SSO1 and SSOa, the average Fmin improvement rate (AIO) is given in Figure 4, where AIO goes from ABC to SSO1, i.e. AIO(ABC, SSO1), defined as follows:

The difference in F _min between ABC and SSO1 was measured by AIO(ABC, SSO1) to improve one F _min unit in SSO1, i.e. the higher AIO(ABC, SSO1), the more efficient SSO1 and vice versa. For example, for T=3.75 in Figure 4, AIO(ABC, SSO1)=55.673% indicates that a one-unit improvement in the mean _Fmin of SSO1 will result in a 0.55673 increase in the difference between the mean _Fmin of ABC and SSO1. Likewise, AIO(SSOa, SSO1) and AIO(ABC, SSOa) can be obtained.

As can be seen from Figure 4, the value of AIO(ABC, SSO1) increases from -21.227% (worst) for T=1.25 to 55.673% (best) for T=3.75; AIO(ABC, SSOa) increases from T=1.25 48.396% of (best) dropped to 4.936% at T=3.25 (worst) and then increased to 29.960% at T=3.75. Therefore, the following conclusions can be drawn:

1. The performance of SSO1 is always much faster than that of ABC, i.e. when T increases, ABC does not improve to the same extent compared to SSO1 of F _avg .

2. From T=1.25 to T=3.25, the average _Fmin improvement for SSOa tends to be similar to the average improvement for SSO1. However, after T=3.25, the performance of SSO1 improved more than that of SSOa.

3. The quality and robustness of the solution of SSOa exceeds that of ABC.

The reason for these conclusions is that the third UM "scout" is not very effective at evading local optima, since ABC is designed to randomly regenerate the current solution if it does not improve in a predetermined number of iterations. Furthermore, UM _a used in SSOa requires updating all variables, which makes it more robust in global search, but gradually and slowly improves the quality of its solution.

Success rate:

Figure 5 shows that the success rate of the correlation value is at most 0.0001 greater than the exact solution, which is desirable because the correlation value should be as close as possible to the exact value. Figure 5 shows observations similar to those shown in Figure 7. For patients with T<2.75, ABC had better success rate, but for _Fmin , SSO1 always had better success rate.

Effect:

Table 4 mainly shows the calculation number of fitness function to compare the efficiency among ABC, SSO1 and SSOA.

N _ABC is the total number of computations of the fitness function, and n _ABC is the number of computations to obtain the best final solution from ABC. The pair of N _SSO1 and n _SSO1 and the pair of N _SSOa and n _SSOa are parallel to N _ABC and n _ABC in the sense that they are related to each other, since both components of each pair are derived using the same algorithm (N _SSO1 and n _SSO1 from algorithm SSO1 and N _SSOa and n _SSOa from algorithm SSOa.)

In Table 4, the ratio _nABC / _NABC is less than 42%, that is, after 42% of the number of computations of the fitness function of ABC, the final optimal solution never changes. Furthermore, the ratio n _ABC /N _ABC decreases as the running time increases. These two observations further confirm that ABC is well suited for local search but weaker for global search. Both the ratio N _SSO1 /N _ABC and the ratio N _SSOa /N _ABC have values greater than 918, and both nSSO1 /nABC and n _SSOa /n _ABC have values of at least 2,100. Therefore, both UM ₁ and UM _a are at least 918 times faster than the UM implemented in ABC, ie, UM ₁ and UM _a are more efficient than ABC. The ratios of n _SSOa /N _SSOa and n _SSO1 /N _SSO1 in Table 4 are at least 95.5% and 95.47%, respectively. Thus, in contrast to ABC, SSO1 and SSOa continue to improve their solutions almost at the end of their respective runs, ie SSO1 and SSOa are very strong global search algorithms.

Based on these observations, SSO1 achieves a better balance between exploration and utilization compared to ABC and SSOa.

in conclusion:

In the embodiment of the present disclosure, UM ₁ updates a variable in each solution to improve the exploration ability of SSO, and introduces a new HSS to replace the fixed step size to improve the utilization ability of SSO.

Through an extensive experimental study of 18 high-dimensional functions, the resulting HSS with Δ=1.25 achieves better performance than Δ=1.00 and Δ=1.50. Furthermore, the proposed UM1 uses the proposed HSS for Δ = 1.25, achieving a better compromise between exploration and exploitation than ABC, GA, PSO and SSOa.

Note: ABC always has a smaller bias, which makes it more robust than SSO1 and SSOa, since it is less likely to fall into local optima than SSO1 and SSOa.

However, the proposed algorithm in this disclosure still has some limitations, however, there are still some limitations for the proposed algorithm, even including ABC, GA, PSO, SSOa and all current soft computations: a) Some problems in analyzing benchmarks , the configuration that is considered to be globally optimal does not have the highest performance; b) the proposed heuristic method requires knowledge of the limits (upper and lower bounds) of the optimal value. Therefore, the proposed algorithm must be improved to overcome the two main obstacles mentioned above.

Although the results of the proposed algorithm in this disclosure are superior to ABC and SSOa both in terms of solution quality and efficiency. The algorithms proposed in this disclosure may be sensitive to constant parameters. Therefore, considering the evolution process of SSO, its sensitivity aspect will be explored in future work to tune the step size.

Abbreviations/Terms

Δ represents the step size (step length);

ρ _k represents the uniform random number created by the kth (kth) variable in [0,1];

ABC stands for artificial bee colony algorithm;

AOI means F _min average F _min improvement rate;

F(X _i,j ) represents the fitness function of X _i,j ;

gBest represents the best solution in history;

pBest represents the best solution in its own history;

F _avg represents the average fitness of the 50 best gBests;

Fmax represents the worst fitness among the 50 best _gBests ;

F _min represents the best fitness of the 50 best gBest;

F _std represents the fitness standard deviation of the 50 best gBest;

GA stands for Genetic Algorithm;

g _k represents the kth (k ^th ) variable of P _gBest ;

N _● represents the average number of fitness evaluations of the algorithm ●;

n represents the average number of fitness evaluations of the final _gBest that finds the algorithm ;

N _avg represents the average number of fitness evaluations;

n _avg represents the average number of fitness evaluations to find the final gBest;

N _gBest indicates the number of gBest;

N _gen represents the genetic algebra;

N _run represents the number of independent runs;

N _sol represents the number of solutions;

N _var represents the number of variables;

P _gBest represents the current gBest (the best solution in history);

P _i represents the current pBest of the ith (i ^th ) solution (its own historical best solution);

p _i,j represents the jth (j ^th ) variable of P _i ;

PSO stands for particle swarm optimization algorithm/particle swarm optimization algorithm;

SSO stands for Simplified Swarm Optimization Algorithm / Simplified Swarm Algorithm;

T represents the running time limit;

UM ₁ represents a univariate update mechanism;

UM _a represents the full variable update mechanism;

X _i,j represents the i(i ^th ) solution of the j(j ^th ) generation;

x _i,j,k represents the kth (k ^th ) variable of X _gen,sol ;

X _gen,sol represents the sol-th solution of the gen-th generation.

Claims (6)

1. a harmonic group optimization method, is characterized in that, described method comprises the following steps: Step 1, construct the harmonic step size strategy HSS; Step 2, establishing a univariate update mechanism UM ₁ ; In step 3, the optimized SSO is obtained by continuously simplifying the group optimization SSO through UM ₁ and HSS optimization; Step 4, apply the optimized SSO to big data processing. 2. a kind of harmonic group optimization method according to claim 1 is characterized in that, in step 1, the method for constructing harmonic step size strategy HSS is: constructing the HSS based on harmonic sequence as shown in the following formula:

Among them, N _var is the number of variables, U _k and L _k are the upper and lower limits of the kth variable, i is the current algebra, and k is the index of the current variable; if 1,1/2,1/3,1 The sequence of /4, is called the harmonic sequence, and the HSS based on the harmonic sequence can be expressed as follows:

If each inherited cycle lasts for 50 generations, the value of the step size Δi _,k decreases from generation to generation from generation to generation. 3. a kind of harmonic group optimization method according to claim 1 is characterized in that, in step 2, the method for establishing single-variable update mechanism UM ₁ is: only update a random selection in UM ₁ of each solution variables, assuming i is the current generation number, x _{j, k} are variables randomly selected from the jth solution X _j ,

is the time solution obtained by modifying x _{j ,k} of X j, the following equation can be obtained:

σ _k,1 and σ _k,2 are uniform random variables generated in [-0.5, 0.5] and [0,1], respectively; ρ _k is a uniform random variable generated in [0,1]; g _k represents the kth (k ^th ) variable of P _gBest ; L _k and U _k are the lower and upper bounds of the kth variable, respectively. 4. a kind of harmonic group optimization method according to claim 2 or 3 is characterized in that, in step 3, the method that obtains the optimized SSO by UM ₁ and HSS optimization continuous simplified group optimization SSO is the following steps : Step 0, let i=j=gBest=1. Step 1, pass X _j and calculate F(X _j ); Step 2, if F(X _gBest )<F(X _j ) then let gBest=j; Step 3, if j<N _sol , let j=j+1 and go to step 1; Step 4, let n ^* =1, N ^* =50, and let

Wherein, k=1,2,..., _Nvar ; Step 5, let i=i+1 and j=1; Step 6, randomly select a variable from X _j , such as x _j,k ; Step 7, let

Step 8, let

Step 9, if F(X ^* )<F(Xj) then make _{Xj =} X ^* and go to step 10, otherwise go to step 11; Step 10, if F(X _j )<F(X _gBest ), let gBest=j; Step 11, if the current running time is equal to or greater than T, the process ends, and X _gBest is the final solution suitable for F(X _gBest ); Step 12, if j<N _sol then let j=j+1, and go to step 6; Step 13. If i<N ^* then go to step 5; Step 14. Increase n ^* by 1, increase N ^* by 50, and let

where k=1,2,..., _Nvar , and go to step 5. 5. the application of a kind of harmonic group optimization method described in claim 4 in big data processing by artificial neural network, it is characterized in that, the method of application is: Step A1, collecting big data that conforms to the big data type; Step A2, preprocessing and cleaning the collected big data, and then extracting the data set obtained after cleaning the big data; Step A3, dimensionality reduction is performed on the data set obtained after cleaning; Step A4, dividing the data set after dimensionality reduction into a data set into a training set and a test set; Step A5, determine an artificial neural network with a structure of 6-5-1 three-layer perceptron neural network, the neural network needs a total of 41 parameters to be optimally designed, and the value range of the optimal design parameters of the neural network is [-1,1 ]; Step A6, determine that the input variable of the artificial neural network is big data that conforms to the big data type, and the output variable of the artificial neural network is the big data output; Step A7, determine the input variable and the output variable of the artificial neural network; Step A8: Decode the variables in X _j in each optimized SSO into the parameters to be optimized by the artificial neural network, calculate the error of the neural network after training the training set and/or the test set, and calculate the calculated error. As the fitness F(X _j ), it is input into the optimized SSO, and the final solution X _gBest suitable for F(X _gBest ) obtained from the running results of the optimized SSO is decoded into the parameters of the artificial neural network, and will be obtained The artificial neural network is used as a classification model; Step A9: Classify the newly collected big data conforming to the big data type by using the classification model. 6. the application of a kind of harmonic group optimization method described in claim 4 in big data processing by support vector machine, it is characterized in that, the method of application is: Step B1, collecting big data conforming to the big data type; Step B2, preprocessing and cleaning the collected big data and extracting features to obtain a feature vector of the big data; Step B3, the feature vector of the big data is used as the training data set; Step B4, randomly generate j uniform random variables, the set of random variables is X _j , and each randomly selected variable in X _j stores the penalty factor C of the support vector machine and the radial basis kernel parameter g; Step B5: Calculate the fitness F(X _j ) of X _j , input it into the optimized SSO, and decode the final solution X _gBest suitable for F(X _gBest ) obtained from the running result of the optimized SSO into a support vector machine parameters, and use the obtained support vector machine as a classification model; Step B6: Classify the newly collected big data conforming to the big data type by using the classification model.

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